I posted an answer to something similar today, but it was about memorial tattoos, so I'll just past the bfing part here:

You can get a tat and bf, HOWEVER, you should wait until your baby has been eating a variety of solid foods, without reaction. Basically the only reason tat artists won't do them on a bfing mother is because of the tiny, tiny risk of the baby being allergic to the ink (blue and white are the most "allergenic" colors)... I know a few artists, and none will tattoo a nursing mom's BREAST, but will tattoo anywhere else as long as the new baby hasn't had any signs of allergies and is close to a year old. Others will say because of the risk of Hep B infection, staph, etc, but any good tattoo shop will have measures to prevent those-- and your own aftercare can lower that chance as well (keep it moist and sealed with tattoo goo or the like to prevent infection once you leave the parlor). Other places don't buy into it and will gladly tattoo you reguardless of bfing, but you should be honest with the artist and respect their opinion if they choose NOT to give you a tat.

Get to know your tattoo artist! He/she should give you a consultation. If you have a design, bring it with you (it may have to be resized, or detail taken out because of the tools used for tats). Any artist worth their salt will spend time drawing, redrawing, and discussing it with you before you ever sit in the big chair. Drop by the shop occasionally- watch to make sure they clean stations between patrons and use an autoclave (little metal oven) to sterilize all tools. When they get inks out for a new person, they should squirt them into smaller cups and CHANGE GLOVES between people. You should be able to find an artist that makes you comfortable-- and definately check out more than one shop before deciding which artist to go with.